1. Field of the Invention
This invention relates generally to optical interconnections and more specifically to cost-effective side-coupling interconnections using polymer fiber optics.
2. Discussion of the Prior Art
Market pressure has led optical fiber companies to recognize that polymer optical fibers (POFs) could be a promising cost-effective physical layer networking solution of the future. Recent research and development indicates that some large core (&gt;0.5 mm) POF solutions can deliver Gbit/s optical data over 100 meter distance. See, for example, Y. Koike et al. (1995) "High-bandwidth graded-index polymer optical fiber" IEEE J. Lightwave Technology 13: 1475-1489 and S. Yamazaki et al. (1996) "A 2.5 Gb/s 100 m GRIN plastic optical fiber data link at 650 nm wavelength" Graded Index POF Boston: Information Gatekeepers: 98-101. Research is also being conducted to identify methods to fabricate low-cost and low-loss POF's for long wavelengths. See, for example, T. Ishgure et al. (1994) "Large-core high-bandwidth polymer optical fiber and its applications" Technical Digest of CLEO/EUROPE '94: paper CThD5. The POF technology is expected to provide the following significant cost advantages over its glass optical fiber (GOF) counterparts in many areas from raw material cost to processing and connection costs.
Due to a high melting temperature and rigidity, it is difficult (although possible in principle) to etch structures on glass materials. Research has been performed to etch a single micro-mirror into a conventional GOF. See, for example, D. J. Ripin et al. (1995) "High efficiency side-coupling of light into optical fibers using imbedded v-grooves" Electron. Lett. 31: 2204-2205. However, the corresponding low-cost volume production process is not available. In the past, optical couplers coupling light into or out of a GOF were prefabricated in a controlled environment. Methods of using prisms or blazing gratings attached to fibers, using evanescent waves and using electromagnetic mode coupling concepts are the most popular light coupling approaches.
The coupling mechanism of a sequence of uni-directional, mirror-based side couplers can be modeled using the geometry of FIG. 1(a). Here the two sets of marked parameters are: .alpha..sub.i (1.ltoreq.i.ltoreq.N) which are mirror reflective coefficients and .gamma..sub.i which are receiving fiber's transmission coefficients at outputs, both are smaller than or equal to unity. For limited POF length, its absorption and scattering can be omitted. Letting P.sub.i be the output power at the i.sup.th port, it can be shown that the receiving power at the N receiving ports are: EQU P.sub.1 =.alpha..sub.1 .gamma..sub.1 P.sub.in, EQU P.sub.2 =(1-.alpha..sub.1).alpha..sub.2 .gamma..sub.2 P.sub.in,(1) EQU P.sub.N =(1-.alpha..sub.1)(1-.alpha..sub.2) . . . (1-.alpha..sub.N-1).alpha..sub.N .gamma..sub.N P.sub.in.
A uniform power distribution to N ports implies that: ##EQU1## The residue output power P.sub.out is defined as EQU P.sub.out =(1-.alpha..sub.1) (1-.alpha..sub.2) . . . (1-.alpha..sub.N)P.sub.in (3)
Using Equation (2), we have ##EQU2## There exist at least two ways to solve for .alpha.'s and .gamma.'s. The first case is the constant-.gamma. case, which requires .gamma..sub.1 =.gamma..sub.2 = . . . =.gamma..sub.N =.gamma..ltoreq.1. The simplest possible situation is that .gamma.=1, which corresponds to either a perfect coupling or a situation where light is coupled to free-space. The coefficients .alpha. can then be evaluated as: ##EQU3## Correspondingly, the power outputs are: ##EQU4## For example, let P.sub.out =0, we then have .alpha..sub.1 =1/N, .alpha..sub.2 =1/(N-1), . . . .alpha..sub.N-1 =1/2, and .alpha..sub.N =1.
The second case is relevant for fiber-to-fiber coupling where receiving coefficients .gamma.s may not be identical. In this case, by letting .alpha..sub.1 =.alpha..sub.2 = . . . .alpha..sub.N =.alpha. in a so-called constant .alpha. situation, the relation between input and output power is: ##EQU5## where j, like i, is a port index and where j&gt;i to guarantee the validity of equation 8(b). In the most efficient coupling case, let .gamma..sub.1 =1. We then have: ##EQU6## Although the balanced power is reached, this scheme requires a non-zero P.sub.out /P.sub.in and thereby leads to inefficient usage of power. For example, for a pre-determined ratio P.sub.out /P.sub.in, Equation (7) first yields an .alpha. value. Using Equation (8), .gamma. values can then be determined as .gamma..sub.i =(1-.alpha.).sup.N-i, for 1.ltoreq.i.ltoreq.N. The most general case is when neither .alpha. nor .gamma. is a constant. Equations (1) and (2) have to be used to calculate for each coupler. Since there are 2N constants to be decided, a general procedure is for a required P.sub.N, first determine all 0.ltoreq..alpha..sub.i .ltoreq.1 (1.ltoreq.i.ltoreq.N) and .gamma.N using the last equation in Equation(1). Corresponding to the set of N+1 constants, the remaining .gamma..sub.i (1.ltoreq.i.ltoreq.N-1) can be calculated using Equation (2). As a numerical example, letting P.sub.out =0.1 P.sub.in and N=16, we have calculated both constant-.alpha. and constant-.gamma. cases and plotted the parameters .alpha., .gamma., .eta.=P.sub.i /P.sub.in in FIG. 1(b) where .eta. is defined as the power ratio between the ith port and the input. Squares and triangles denote the curves for constant .alpha. and constant .gamma., respectively. It can be seen that since .gamma. could be as large as unity, the overall coupling efficiency for the constant-.gamma. case is, in general, larger than that of the constant-.alpha. case.
Couplings between POF & Free-space: One simple but useful application of using micro-mirrors along a POF is to deliver equal intensity optical signals to N different locations along a fiber. Previous methods of delivering optical signals were reported using either holograms, stacked birefringent crystals and integrated optical wave-guides. See, for example, J. W. Goodman et al. (1980) "Optical inter-connections for VLSI systems" Proc. IEEE 72: 850-858; R. T. Chen et al. (1992) "Guided-wave planar optical inter-connects using highly multiplexed polymer waveguide holograms" J. Lightwave Tech. 10: 888-897; J. Jahns (1994) "Diffractive optical elements for optical computers" Optical Computing Hardware, eds. J. Jahns and S. H. Lee, New York: Academic Press: 137-167; and T. W. Stone et al. (1994) "Optical array generation and Interconnection using birefringent slabs" Appl. Opt. 33: 182-191. The availability of a POF splitter can provide a flexible yet low-cost method and apparatus for delivering optical signals to receiving terminals with flexible spacings than the above mentioned situations. See, for example, Y. Li et al. (1996) "4.times.16 polymer optical fiber array couplers" IEEE Photon. Tech. Lett. 8: 1650-1652.